Question

Assessing return and risk???Swift Manufacturing is evaluating an asset purchase. The annual rate of return and the related probabilities given in the following table summarize the? firm's analysis to this? point:

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a.??Compute the range of possible rates of return.

b.??Compute the expected return.

c.??Compute the standard deviation of the returns.

d.??Compute the coefficient of variation of the returns.

Table:

Rate of return	Probability
55%	0.05
10?%	0.05
15?%	0.10
20?%	0.10
25?%	0.35
30?%	0.15
35?%	0.10
40?%	0.05
45?%	0.05

Answer 1

a. Range =

In statistics, the range of a set of data is the difference between the largest and smallest values.

Largest value = 0.35

Smallest value = 0.05

Hence, range = 0.35 - 0.05 = 0.30

b. Excpected Return = 27.75%

Rate of return (Col. A)	Probability (Col. B)	Probability * Rate of Return (Col. C = Col. A * Col. B)
55%	0.05	0.0275
10%	0.05	0.005
15%	0.1	0.015
20%	0.1	0.02
25%	0.35	0.0875
30%	0.15	0.045
35%	0.1	0.035
40%	0.05	0.02
45%	0.05	0.0225

Expected Return (Sum of all values in col. C in table above) = 27.75%  

c. Standard Deviation = 10.305%

Rate of return	Probability	Deviation from Expected Return	Squared Deviation	Probability * Squared deviation
55%	0.05	= 0.55 - 0.2775 =0.27250	0.07426	0.00371
10%	0.05	= 0.1 - 0.2775 = -0.17750	0.03151	0.00158
15%	0.1	= 0.15 - 0.2775 = -0.12750	0.01626	0.00163
20%	0.1	= 0.2 - 0.2775 = -0.07750	0.00601	0.00060
25%	0.35	= 0.25 - 0.2775 = -0.02750	0.00076	0.00026
30%	0.15	= 0.3 - 0.2775 = 0.02250	0.00051	0.00008
35%	0.1	= 0.35 - 0.2775 = 0.07250	0.00526	0.00053
40%	0.05	= 0.4 - 0.2775 = 0.12250	0.01501	0.00075
45%	0.05	= 0.45 - 0.2775 = 0.17250	0.02976	0.00149

Standard deviation = Square Root of Sum of all Squared deviation

Sum of all squared deviations = 0.01062

Standard deviation = square root of 0.01062 = 0.10305 = 10.305%

d. A coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. It is calculated as follows: (standard deviation) / (expected value)

CV = 10.305%/27.75% = 0.3713